Question

Consider a one year American put option on 100 ounces of gold with a strike of $2300 per ounce. The spot price per ounce of gold is $2300 and the annual financing rate is 7% on a continuously compounded basis. Finally, gold annual volatility is 15%. U= 1.112, D=0.8994, U= 0.6411. In answering the questions below use a binomial tree with two steps.

A. Value the option at time 0 using the binomial tree.

B. How would you hedge a long position in the put option at time 0 with a portfolio composed of a position in gold, and a cash borrowing or lending position?

Answer 1

Thus Put premium is $80.27

Ans 2: Amount required for Buying Put option is $80.27*100 = $8027

To hedge this position, We require Short position in Gold and lend money to bank

At node (0,0)

Short Position required = (pu-pd) / (Su-Sd) = (0-231.38) / (2557.6-2068.62) = -0.47

Short 0.47*100 = 47 ounce gold.

Lend 47*2300 - 8027 = 100,073 to be lended to bank

After 6 month, amount in bank will become 100,073*e(0.07*0.5)=103,637.57

At node (0,1), = (0-0)/(2844-2300) = 0, No position in Gold required

At node (1,1) = (0-439.48)/(2300-1860.52) = -1

So Short 100 Ounce of gold and use the proceed to deposit in bank = 100*2068.62 = 206,862